Pinned Questions of logic/mathematics/lateral thinking

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    • Dear friend:

      Soon after buying this old mansion, I had the unpleasant surprise to see that it is bewitched by two sounds from beyond the grave, which make it practically uninhabitable: a picaresque song and a sardonic laugh.

      I still have some hope, however, because experience has shown me that their behavior obeys certain dark but infallible laws that can be modified by touching the organ and burning incense.

      In each minute, each sound is present or absent: what each of them will do in the next minute depends on what happens in the current minute in the following way:

      The song will keep the same state (present or absent), except if during the current minute there is no laughing and the organ is played, in which case the singing takes the opposite state.

      As for laughter, if I do not burn incense, it will be heard or not according to whether the song is present or absent (so that laughter imitates the song with a miute of delay). Now, if I burn incense, laughter will do just the opposite of what I was singing.

      The moment I write to you, I am hearing both laughter and singing. I will be very grateful if you tell me that organ and incense manipulations should continue to restore calm.

      Because my will is as strong as yours and my kingdom as great ...

      You have no power over me.
    • In a railway line, the track has a double track except in a tunnel, which is not wide enough to accommodate both.

      Therefore, in the tunnel, the line is single track. One afternoon, a train entered the tunnel marching in one direction, and another train in the same tunnel, but in the opposite direction. Both were going at full speed, and yet they did not collide.

      Explain it!.

      Because my will is as strong as yours and my kingdom as great ...

      You have no power over me.
    • Imagine there’s an island where a mad dictator holds 100 people captive, and all of them are great mathematicians. They can’t escape, but there is one strange rule governing their captivity. At night, any prisoner is allowed to ask the guard for his freedom. If he has green eyes, he’ll be released, otherwise he’ll be dropped into a volcano.

      It turns out that all 100 prisoners have green eyes. But they’ve all been living on the island since they were born, and the dictator has done all that he can to ensure that none of them will ever be able to find out what color eyes they have. There are no mirrors on the island, and all water visible to the prisoners is opaque — thus they cannot see their reflection. And most importantly, the prisoners are not allowed to communicate among themselves.

      Nevertheless, they see each other at roll call every morning. Everybody knows that no one will dare ask for their freedom unless they are absolutely sure of their success. Under considerable pressure from human rights organizations, the dictator was forced to permit you to visit the island and speak to the prisoners, but only under the following conditions. You may only make one statement, and you can’t provide them with any new information. So how can you help the prisoners without breaking the agreement with the dictator?.

      After much thought, you tell the crowd: ‘At least one of you has green eyes’. The dictator is very suspicious, but he is sure your statement won’t change anything. You leave, and the life on the island seems to continue along its usual course. But one morning, 100 days after your visited, the island suddenly becomes empty — the previous night, all the prisoners asked to leave.

      So how did you manage to outsmart the dictator?.

      Because my will is as strong as yours and my kingdom as great ...

      You have no power over me.
    • The White House also pointed to the fashion of mathematical problems. Edward Felten, the signing of Obama as deputy director of technology in Washington, opened with a riddle on the blog of the government agency.

      With this challenge, Felten aims to demonstrate to Internet users that information technology is "something more than putting code" and that in fact "can help solve social problems" and teach society to relate better and cooperate in the resolution of complex problems.

      The problem is the following:

      "Alice and Bob are playing a game, they are teammates so they either win or lose together. Before the game starts, they can talk to each other to design a strategy.
      When the game begins Alice and Bob get into separate and soundproof rooms. They can not communicate with each other in any way. Both throw a coin in the air and write down if it comes up heads or tails (and they can not lie).

      Then Alice writes down what she thinks has come to Bob and vice versa. If one or both of them are right, Alice and Bob win. But if they fail, both will lose.

      Are you able to design a strategy so that the two always win?".

      Because my will is as strong as yours and my kingdom as great ...

      You have no power over me.
    • Albert and Bernard ask Cheryl when her birthday is, but she has an enigmatic day, so instead of answering them as she would, anyone decides to make them nervous and give them a list with ten possible dates: May 15, May 16, 19 May, June 17, June 18, July 14, July 16, August 14, August 15, August 17.

      Later, Cheryl tells Albert and Bernard separately the month and the day, respectively.

      Then Albert says: "I do not know when Cheryl's birthday is, but I know Bernard does not know either." To which Bernard responds: "At first I did not know when Cheryl's birthday was, but now I know." Albert reflects and concludes: «Then I also know when his birthday is».

      When is Cheryl's birthday?

      Because my will is as strong as yours and my kingdom as great ...

      You have no power over me.
    • Hello Charlie!. Welcome to the thread of Questions of logic/mathematics/lateral thinking.

      You can use Python, JAVA, C/C++, Golang, Assembler X86, or any other language you want, but you have to guess the answer ...

      How many circles do you see in this image ?:


      Because my will is as strong as yours and my kingdom as great ...

      You have no power over me.